Question

Which of the following is a polynomial?

• A. \(x^2-6\sqrt x+2\)
• B. \(\frac {5}{x^2-3x+1}\)
• C. \(5x^2-3x+\sqrt 2\)
• D. \(2x^2-\frac 5x+3\)

Answer 1

The Correct Option is C

A polynomial must satisfy three conditions:

1. Variables must have non-negative integer exponents
2. No variables in denominators
3. No variables under roots

Option (1): x² - 6√x + 2
This fails condition 3 because √x = x^1/2 has a fractional exponent.

Option (2): 5/(x⁴ - 3x + 1)
This fails condition 2 because variables appear in the denominator.

Option (3): 5x² - 3x + √2
This satisfies all conditions:

• Exponents are integers (2, 1, 0)
• √2 is a constant coefficient
• No variables in denominators or roots

Option (4): 2x² - 5/x + 3
This fails condition 2 because 5/x = 5x^-1 has a negative exponent.

Therefore, the correct answer is: (3) 5x² - 3x + √2